The 22-year-old fly-half was handed his Premiership debut in the red-hot atmosphere of an east midlands derby that was crucial for both sides.
Myler kept his composure to kick a penalty and conversion that wrapped up a historic Welford Road win and handed the Saints a huge boost in their battle to beat the drop.
Grayson said: "He kept us going and has a big future. He has that air of quality that makes it look like he has time on the ball in pressured situations."
Northampton had lost six of their previous seven games but Myler's kicking and a stunning try from Mark Robinson were enough to cancel out Ian Humphreys' three penalties for the hosts.
Grayson said: "There's a bit of relief in the dressing room, but this is just one step on a difficult journey.
"Wins here are always precious and the fact that they had so many internationals missing gave us a chance.
"We didn't play a lot of rugby in the second half, but we played with a lot of passion and attitude and that's half the battle.
"We gave away enough penalties for them to win the game but we got away with it."
Grayson believes his players went into the game under no pressure.
He said: "We came here with no expectations from anyone. We were big underdogs and sometimes that allows you to throw off the shackles.
"We would have got a pat on the back even if we had lost the game at the end.
"We are desperate for points and will fight like hell to get out of the situation we are in."
Leicester head coach Pat Howard offered no excuses for his side's first home defeat in the Premiership since January 2004.
He refused to use the absence of six internationals as an excuse, saying: "We have a strong enough squad to win regardless.
"But we constructed so little and I'm extremely disappointed.
"That's two weeks in a row when missed opportunities have cost us.
"We could have finished off a few things, but we lost our way.
"I think that's the worst performance since I have been at Welford Road."